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In this last lecture I would like to give

a deeper insight on organic field effect transistors or OFET.

In our previous lecture we have analyzed first

qualitatively and then quantitatively the output curves of an OFET,

making a distinction between the linear and saturation regimes.

Another way to graphically represent the performance

of a transistor is the so-called transfer curve,

when the drain current is plotted as a function of

the source gate voltage for a given source drain voltage.

The transfer curve is usually plotted in a semi-log scale.

The threshold voltage appears as a transition point between

an exponentially varying domain,

and a region where the drain current is linear or quadratic.

The 'above threshold' or 'on current' is the domain where the device is used in practice.

Below threshold the current increases

exponentially so we can define a sub-threshold slope.

Finally, the off-current is mainly due to various leaks.

Transistors are mainly used as ultra-fast switches.

The figures of merit are the current they can deliver and their switching speed.

The switching time can be defined as the time it takes for

its charge to go from the source to the drain,

that is, the channel length L divide by the mean velocity of the charges.

Recalling that the mean velocity is the mobility times

the electric field and assuming the field is uniform in the channel,

we find that the switching time is proportional to the channel length,

to the square, and inversely proportional to the mobility.

So, to reduce the switching time one can

alternatively reduce the channel length or increase the mobility.

Mobility is a crucial parameter in transistors.

This is why research largely focuses at improving the mobility.

Taking the representative example of pentacene,

we can see the two stages in the evolution of the mobility.

Up to the late 1990's the mobility increased steadily.

This actually came from improvements of both the

material itself and the fabrication of the device.

Since then there is a sort of leveling off

suggesting that the limits of the compound has been reached.

The current state of the art is as follows.

For crystalline silicon the mobility is around 1,000 centimeter per volt and per second.

Poly-crystaline silicon is useful in large area applications.

Its mobility is around 10 times lower.

For OFETs, the mobility value range between one and

10 for p-channel and 0.1 and 1 for n-channel devices.

Extracting the mobility of the transistors is an important issue.

This is done from the transfer curve.

In the linear regime,

when the source drain voltage is much lower than the source gate voltage,

the drain current is linear with the source gate voltage

so the mobility can be estimated from the slope of the straight line.

In the saturation regime,

when the source drain voltage is larger than the source gate voltage,

the drain current now varies as the square of the source gate voltage.

So now we plot the square root of the drain current,

and once more, the mobility is given by the slope of the straight line.

However, in practice, the transfer curve does not always obey these simple rules.

Two additional issues must be taken into account for a correct parameter extraction,

contact resistance and gate voltage dependent mobility.

Contact resistance is an issue that affects all kinds of electronic devices.

It comes from the fact that charge carrier have to pass

a barrier when injected from a metal to a semiconductor.

In the transistor, the usual way to represent

contact resistance is to add resistors between the contact and the device.

So there is a resistance,

R_s at source and R_d at drain.

In practice, the contact resistance R_c is the sum of these two resistances.

Mathematically speaking, contact resistance induces

a voltage drop equal to the resistance times the current.

In the linear regime,

the equation now contains I_d at both sides.

Simple mathematics leads to this equation where the

current is no longer proportional to the source gate voltage.

So the effect of the contact resistance can be shown

by plotting the transfer curve in the linear regime.

In the absence of contact resistance the curve is a straight line,

but adding a contact resistance, curbs the curve downward.

The second issue is more specific to organic semiconductors.

Charge transport models with localized states predict that

mobility increases with the density of charge carriers.

So mobility also increases with the source gate voltage.

A useful semi-empirical description of the dependence is

through a power law with a positive exponent gamma.

Now we see that gate bias dependent mobility curbs the transfer curve upwards.

In practice, both effects may be present so extracting

the real mobility often requires additional investigations.

However, mobility is not the only parameter to account for.

Transistor are used in circuits that include thousands,

millions or even billions of devices.

Designing the circuits cannot be conducted by trials and errors.

The design is actually made through computer assisted design or CAD,

which requires a comprehensive set of equations to fully describe the transistors.

This ends the course on organic electronics.

I thank you for your participation.